Cellular Automata as an Alternative to (Rather than an Approximation of) Differential Equations in M

Abstract Cellular automata are models of distributed dynamical systems whose structure is particularly well suited to ultrafast, exact numerical simulation. On the other hand, they constitute a radical departure from the traditional partial-differential-equation approach to distributed dynamics. Here we discuss the problem of encoding the state-variables and evolution laws of a physical system into this new setting, and of giving suitable correspondence rules for interpreting the model's behavior.